One of the most satisfying aspects of condensed matter physics is that a variety of condensed matter systems show universal behavior—behavior that appears to be common to a wide variety of unrelated systems. The phenomenon of “jamming,” which is similar to what happens to vehicles in traffic jams, fits into this category. Recent ALS research has revealed that even magnetic domains behave very much like other granular material systems, and their dynamical behavior mimics the universal characteristics of several jammed systems.

Jamming Transitions Give Insight into Behaviors

Recently, there has been much interest in jamming transitions, which were originally studied as a way to discuss the behavior of granular materials or dense assemblies of particles but have been eventually proposed as a more general and unified way of looking at dynamics of systems as diverse as structural glasses, entangled polymers, colloidal gels, supercooled liquids, and the like. Jamming is the physical process by which some materials become rigid with increasing density. Jamming occurs when the particle densities or entanglements are such that the motions of the individual particles become very restricted so that they slow down. The fluctuations that occur in a jammed system with long-range interactions are cooperative fluctuations where a local displacement causes an inhomogeneity, which is correlated with a displacement in another region.

Schematic showing the use of coherent x-rays to obtain magnetic speckles from the spiral antiferromagnetic dysprosium.

In systems with a particle density above a threshold value, a jamming transition occurs wherein the motion of particles is restricted and also correlated to the motion of the surrounding ones. This type of jamming behavior is universal to a variety of systems such as granular materials, gels, polymers, and glasses. At ALS Beamline 12.0.2.2, researchers investigated the size and dynamics of magnetic domains—the volume of ordered electron spins found in magnetic materials—using a technique called “resonant magnetic x-ray photon correlation spectroscopy” that uses coherent x-ray beams (similar to laser light) that have had their energy tuned to resonantly interact with the magnetic moments of the atoms. As the scattered x-ray beams interact with the material, the interference between the scattered waves from the domain boundaries produce a pattern of “speckles”—spots on a fast charge-coupled area detector—whose intensity fluctuates as a function of time. The intensity fluctuations in these speckles are due to the slow movement of the magnetic domain walls and hence the speckle-pattern movie contains information on the size and dynamics of these domains.

The researchers observed the jamming behavior in a rare-earth element, dysprosium, that exhibits an antiferromagnetic spin structure within a certain temperature window (85 – 180 K). In the antiferromagnetic phase, the spins are arranged in a spiral structure, very similar to a spiral staircase. Such a spiral spin structure allowed the researchers to obtain a pure magnetic scattering signal that could be distinguished from charge scattering. The period of the spiral was about 6 – 12 unit cells, depending on the temperature. Using x-rays tuned to the L-edge of dysprosium to selectively look for magnetic x-ray scattering, the researchers obtained a magnetic diffraction peak at Qz = (0, 0 , l ± Qm), where l is an even integer. Q is the momentum transfer in reciprocal space.

Left: The decay time obtained from the autocorrelation function shows a dramatic increase when the temperature is lowered from the phase transition temperature. Right: The decay time is a function of the lateral magnetic domain size. When the temperature is lowered, the domains grow in size and the dynamics slow down.

Just above the Neel temperature (the temperature at which the spins order in their spiral arrangement) many such clusters with different spin directions exist and grow in size, eventually coalescing into magnetic domains. At the Neel temperature, these domains are head-to-head with each other in a jammed state and the domain boundaries form a disordered network. The researchers found that the slow thermal fluctuations of the domain walls exhibited a compressed exponential relaxation with an exponent of 1.5, found in a wide variety of solid-like jammed systems, which could be qualitatively explained in terms of stress release in a stressed network. As the temperature is further lowered a few degrees below the Neel temperature, the domains grow in size and the dynamics progressively get arrested, as happens in all glassy materials. The relaxation times obey the Vogel-Fulcher law as observed in polymers, glasses, and colloids, thereby indicating that the dynamics of domain walls in an ordered antiferromagnet exhibit some of the universal features associated with jamming behavior.

Understanding the quantitative behavior of magnetic domain fluctuations near phase transitions will enable the control of noise levels and help to improve the performance of magnetic nanodevices.

Research funding: Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. Operation of the ALS is supported by the U.S. Department of Energy, Office of Basic Energy Sciences.